Is there a way to use the same functionality as

float: footnote


but without the numbering?

Thanks!

Yes you can disable the footnote marker:

<style>
.fn {
    float: footnote
}

.fn::footnote-call, .fn::footnote-marker {
    content: none
}
</style>
<p>
Some text.
<span class="fn">A footnote.</span>
</p>

Thanks!